Telecommunications systems, cable television systems and data communication networks may use optical networks to rapidly convey large amounts of information between remote points. In an optical network, information may be conveyed in the form of optical signals through optical fibers. Optical fibers may comprise thin strands of glass capable of communicating the signals over long distances with very low loss.
One consideration in analyzing the effectiveness of communicating a signal is the optical signal-to-noise ratio (OSNR). This value may indicate the instantaneous quality of a signal. As a signal passes through a network, it may lose signal strength or may increase in noise, resulting in a decrease of the overall OSNR. If OSNR drops below a certain point, the signal may be unreadable at a desired destination. Thus, it may be desirable to measure OSNR.
OSNR may be represented by the relationship in Equation (1).
                              O          ⁢                                          ⁢          S          ⁢                                          ⁢          N          ⁢                                          ⁢                      R            ⁡                          [              dB              ]                                      =                  10          ×                      log            ⁡                          (                                                P                  sig                                                  P                  noise                                            )                                                          (        1        )            
where Psig represents the power of the signal to be measured (for example, the magnitude of signal strength), and Pnoise represents the power of the noise. For example, for optical signals, this may represent the intensity of light.
Optical networks often employ modulation schemes to convey information in the optical signals over optical fibers. Such modulation schemes may include phase-shift keying (“PSK”), frequency-shift keying (“FSK”), amplitude-shift keying (“ASK”), and quadrature amplitude modulation (“QAM”).
In PSK, the information carried by the optical signal may be conveyed by modulating the phase of a reference signal, also known as a carrier wave. The information may be conveyed by modulating the phase of the signal itself using differential phase-shift keying (“DPSK”).
In QAM, the information carried by the optical signal may be conveyed by modulating both the amplitude and phase of the carrier wave. PSK may be considered a subset of QAM, wherein the amplitude of the carrier waves is maintained as a constant.
PSK and QAM signals may be represented using a complex plane with real and imaginary axes on a constellation diagram. The points on the constellation diagram representing symbols carrying information may be positioned with uniform angular spacing around the origin of the diagram. The number of symbols to be modulated using PSK and QAM may be increased and thus increase the information that can be carried. The number of signals may be given in multiples of two. As additional symbols are added, they may be arranged in uniform fashion around the origin. PSK signals may include such an arrangement in a circle on the constellation diagram, meaning that PSK signals have constant power for all symbols. QAM signals may have the same angular arrangement as that of PSK signals, but include different amplitude arrangements. QAM signals may have their symbols arranged around multiple circles, meaning that the QAM signals include different power for different symbols. This arrangement may decrease the risk of noise as the symbols are separated by as much distance as possible. A number of symbols “m” may thus be used and denoted “m-PSK” or “m-QAM.”
Examples of PSK and QAM with a different number of symbols can include binary PSK (“BPSK” or “2-PSK”) using two phases at 0° and 180° (or 0 and π) on the constellation diagram; or quadrature PSK (“QPSK”, “4-PSK”, or “4-QAM”) using four phases at 0°, 90°, 180°, and 270° (or 0, π/2, π, and 3π/2). Phases in such signals may be offset. This may be extended, for example, up to 16-QAM, using sixteen phases. These various signals (for example, 2-PSK or 16-QAM) may be arranged in one circle on the constellation diagram.
M-PSK signals may also be polarized using techniques such as dual-polarization QPSK (“DP-QPSK”), wherein separate m-PSK signals are multiplexed by orthogonally polarizing the signals.